Module complex_double

File: sage/rings/complex_double.pyx (starting at line 1)

Double Precision Complex Numbers

SAGE supports arithmetic using double-precision complex numbers.  A
double-precision complex number is a complex number x + I*y with x, y
64-bit (8 byte) floating point numbers (double precision).

The field \code{ComplexDoubleField} implements the field of all
double-precision complex numbers.  You can refer to this field by the
shorthand CDF.  Elements of this field are of type
\code{ComplexDoubleElement}.  If x and y are coercible to doubles, you
can create a complex double element using
\code{ComplexDoubleElement(x,y)}. You can coerce more general objects
z to complex doubles by typing either \code{ComplexDoubleField(x)} or
\code{CDF(x)}.

EXAMPLES:
    sage: ComplexDoubleField()
    Complex Double Field
    sage: CDF
    Complex Double Field
    sage: type(CDF.0)
    <type 'sage.rings.complex_double.ComplexDoubleElement'>
    sage: ComplexDoubleElement(sqrt(2),3)
    1.41421356237 + 3.0*I
    sage: parent(CDF(-2))
    Complex Double Field

    sage: CC == CDF
    False
    sage: CDF is ComplexDoubleField()     # CDF is the shorthand
    True
    sage: CDF == ComplexDoubleField()
    True
    

The underlying arithmetic of complex numbers is implemented using
functions and macros in GSL (the GNU Scientific Library), and should
be very fast.  Also, all standard complex trig functions, log,
exponents, etc., are implemented using GSL, and are also robust and
fast.  Several other special functions, e.g. eta, gamma, incomplete
gamma, etc., are implemented using the PARI C library.

AUTHOR:
    -- William Stein (2006-09): first version

File: sage/rings/complex_double.pyx (starting at line 1817)

Returns the field of double precision complex numbers.

EXAMPLE:
    sage: ComplexDoubleField()
    Complex Double Field
    sage: ComplexDoubleField() is CDF
    True    

File: sage/rings/complex_double.pyx (starting at line 466)

Return True if x is a is_ComplexDoubleElement.

EXAMPLES: 
    sage: is_ComplexDoubleElement(0)
    False
    sage: is_ComplexDoubleElement(CDF(0))
    True

File: sage/rings/complex_double.pyx (starting at line 104)

Return True if x is the complex double field. 

EXAMPLE:
    sage: from sage.rings.complex_double import is_ComplexDoubleField
    sage: is_ComplexDoubleField(CDF)
    True
    sage: is_ComplexDoubleField(ComplexField(53))
    False